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Description/Abstract

This paper attempts to unify some of the existing approaches to defining modal logics for coalgebras, from the point of view of constructing the languages employed by these logics. An abstract framework for defining languages for coalgebras from so-called language constructors, corresponding to one-step unfoldings of the coalgebraic structure, is introduced, and a method for deriving expressive languages for coalgebras from suitable choices for the language constructors is described. Moreover, it is shown that the derivation of such languages by means of language constructors is well-behaved w.r.t. various forms of composition between coalgebraic types.